Question

Let A be a 5x3 matrix. Is it possible that rank(AA^T)=4? Why?

Answer 1

\[\text{rank}(AB)\le\min(\text{rank}(A),\text{rank}(B))\]

Answer 2

I don't understand what that means :\ but would it be because the rank of the mxm matrix AAT is m that it is not true??

Answer 3

\[\text{rank(A)}\le 3\]

Answer 4

the rank of a product is less than or equal to the lesser of the two ranks